Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x+3y &= 6 \\ -3x-9y &= 4\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-9y = 3x+4$ Divide both sides by $-9$ to isolate $y$ $y = {-\dfrac{1}{3}x - \dfrac{4}{9}}$ Substitute this expression for $y$ in the first equation. $-x+3({-\dfrac{1}{3}x - \dfrac{4}{9}}) = 6$ $-x - x - \dfrac{4}{3} = 6$ Simplify by combining terms, then solve for $x$ $-2x - \dfrac{4}{3} = 6$ $-2x = \dfrac{22}{3}$ $x = -\dfrac{11}{3}$ Substitute $-\dfrac{11}{3}$ for $x$ back into the top equation. $+ \dfrac{11}{3}+3y = 6$ $\dfrac{11}{3}+3y = 6$ $3y = \dfrac{7}{3}$ $y = \dfrac{7}{9}$ The solution is $\enspace x = -\dfrac{11}{3}, \enspace y = \dfrac{7}{9}$.